Analysis of Raman and neutron scattering spectra of lysozyme demonstrates that the protein dynamics follow the dynamics of the solvents glycerol and trehalose over the entire temperature range measured 100-350 K. The protein's fast conformational fluctuations and low-frequency vibrations and their temperature variations are very sensitive to behavior of the solvents. Our results give insight into previous counterintuitive observations that protein relaxation is stronger in solid trehalose than in liquid glycerol. They also provide insight into the effectiveness of glycerol as a biological cryopreservant.